Course on Biostatistics Instructors – Dr. Małgorzata Bogdan Dr. David Ramsey Institute of Mathematics and Computer Science Wrocław University of Technology Poland

Course on Biostatistics Two parts 1. Locating genes influencing quantitative traits in experimental populations , Małgorzata Bogdan 2. Population Genetics , David Ramsey

Grading Students can gain 50 points for each part of the course (25 for a project, 25 for an exam). The final grade will be based on the total percentage. To pass the course the student has to gain at least 15 points for each part of the course and at least 50 points in total.

First part Locating genes influencing quantitative traits in experimental populations Małgorzata Bogdan

Course Outline Introduction to genetics and experimental populations. Basic methods of locating quantitative trait loci (QTL). Locating QTL with QTL Cartographer.

Helpful materials Text book Genetics and Analysis of Quantitative Traits by Michael Lynch and Bruce Walsh Software – Windows QTL Cartographer S.Wang, C.J. Basten, Z-B. Zeng Program in Statistical Genetics, North Carolina State University Can be downloaded from

Main Goal Learn how to locate regions of the genome hosting genes influencing some quantitative traits (Quantitative Trait Loci – QTL). Statistical methods – mainly linear models.

Introduction to Genetics DNA - A nucleic acid that carries the genetic information in the cell. DNA consists of two long chains of nucleotides joined by hydrogen bonds between the complementary bases adenine and thymine or cytosine and guanine. The sequence of nucleotides determines individual hereditary characteristics.

Introduction to Genetics Chromosome – a ‘’long’’, continuous piece of DNA, which contains many genes, regulatory elements and other intervening nucleotide sequences. Diploid organisms – chromosomes appear in pairs (one from each parent)

Allele - any of two or more alternative forms of a gene that occupy the same locus on a chromosome. Example: allele of blue eyes, allele of brown eyes Genotype at a single locus: the pair of alleles that individual carries at the locus.

The Hardy-Weinberg principle Random mating p a - frequency of a allele p A - frequency of A allele P(aa)=p 2 a P(aA)=2p a p A P(AA)=p 2 A

Phenotype – observed or measured characteristic (or trait) for an individual. We will be dealing with quantitative traits like eg. height, yield, blood pressure etc.

Heritability Z - the phenotypic (trait) value of an individual G – the genotypic value (the sum of the total effects of all loci on the trait) E – an environmental deviation Z = G + E Broad sense heritability (population parameter) H 2 = Var (G) / Var (Z)

The influence of a single locus

Fisher’s decomposition of the Genotypic Value Consider a biallelic locus with alleles a, A N – number of alleles ’’a’’ for a given individual (gene content) We regress G on N Var(G) =  2 A +  2 D

Trait Influenced by Two Loci G ijkl – mean phenotype for individuals with genotypes (i j; k l) α i = G i… -  G - additive effect of i allele δ ij = G ij.. -  G - α i - α j - dominance effects at the first locus δ kl = G kl.. -  G - α k - α l - dominance effects at the second locus

Possible interactions (epistasis) (αα) ik =G i.k. -  G – α i – α k (αδ) ikl = G i.kl. -  G – α i – α k – α l – δ kl - (αα) ik - (αα) il (δδ) ijkl = G ijkl. -  G – α i – α j – α k – α l – δ ij - δ kl - (αα) ik - (αα) il -(αα) jk - (αα) jl - (αδ) ikl - (αδ) jkl - (αδ) ijk - (αδ) ijl

Example (Lynch and Walsh) Teosinte – wild progenitor of cultivated maize Two loci (markers) - UMC107, BV302 U M, B M – maize alleles U T, B T – teosinte alleles Trait – the average length of the vegetative internodes in the lateral branch (in mm)

Mean trait values UMC107 BV302 U MM U MT U TT B MM B MT B TT

Genotype Frequencies UMC107 BV302 U MM U MT U TT B MM B MT B TT

Cockerham model 1

Cockerham model 2

Cockerham model 3 two loci

Genetic maps Markers – genetic loci which express experimentally detectable variation between individuals. Genetic map gives an order of markers on a chromosome and a distance between them. 1 Morgan – the expected value of the number of crossovers is equal to 1

Genetic map

A B xP: AB x B F1: low fat content a b q c d high fat content A B Q C D a b q c d A B Q C D A B q c d A B Q C D a B Q C d A B Q C D a b q c d A B Q C D BC: